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A white nationalist rally on the grounds of the University of Virginia in Charlottesville.CreditEdu Bayer for The New York Times

WASHINGTON — The House and Senate have unanimously passed a joint resolution urging President Trump to denounce racist and anti-Semitic hate groups, sending a blunt message of dissatisfaction with the president’s initial, equivocal response to the white nationalist violence in Charlottesville, Va., last month.

The resolution passed the Senate without dissent on Monday and was approved without objection by the entire House on Tuesday night. It could be sent to the White House for Mr. Trump’s signature as early as Wednesday.

A White House spokeswoman did not immediately answer a request for comment.

The nonbinding measure specifically singles out for condemnation “White nationalists, White supremacists, the Ku Klux Klan, neo-Nazis, and other hate groups.” That represents a sharp contrast to the president’s first comments after the deadly early August demonstrations in which he assigned equivalent blame for the violence on anti-fascist counter-protesters.

Mr. Trump denounced “hatred, bigotry and violence — on many sides” and argued that many of the protesters who staged a torchlight march to protest the removal of a statue of Robert E. Lee from the University of Virginia campus were “very fine people.”

One of the counterprotesters, Heather Heyer, 32, was killed when a white nationalist demonstrator drove a car into a crowd. Two Virginia State troopers died when their helicopter crashed while monitoring the violence that swept through the usually sedate college town.

The House version of the resolution, introduced by Republican and Democratic House members from Virginia, asks Mr. Trump to “use all resources available to the President and the President’s Cabinet to address the growing prevalence of those hate groups in the United States.”

In a rare show of bipartisan unity, Speaker Paul D. Ryan of Wisconsin and Senator Mitch McConnell of Kentucky, the majority leader, introduced the measure as a joint resolution, which requires a presidential signature. Two Republican congressional aides involved in the process said the intent was to put the president on the record calling out white racism by name.

The text doesn’t include any reference to counterprotesters.

It also calls on Attorney General Jeff Sessions to “investigate thoroughly all acts of violence, intimidation, and domestic terrorism by White supremacists, White nationalists, neo-Nazis, the Ku Klux Klan, and associated groups” and to “improve the reporting of hate crimes” to the F.B.I.

“What happened in Charlottesville was an act of domestic terrorism perpetrated by a white supremacist, one that tragically cut short the life of a young woman, Heather Heyer, who was speaking out against hatred and bigotry,” Senator Mark Warner, Democrat of Virginia and a co-sponsor of the measure, said in a statement. “We will be pressing our colleagues to swiftly and unanimously approve this resolution in order to send a strong message that the United States Congress unconditionally condemns racist speech and violence.”